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Localization Algebras and Duality
Author(s) -
Chen Xiaoman,
Wang Qin
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003393
Subject(s) - mathematics , bounded function , conjecture , homology (biology) , duality (order theory) , pure mathematics , metric (unit) , metric space , dual (grammatical number) , hochschild homology , singular homology , mathematical analysis , chemistry , amino acid , philosophy , biochemistry , operations management , cohomology , economics , linguistics
The paper studies the dual algebras of localization Roe algebras over proper metric spaces and develops a localization version of Paschke duality for K ‐homology. It is shown that the localization K ‐homology groups are isomorphic to Kasparov's K ‐homology groups for the Rips complex of proper metric spaces with bounded geometry. It follows that the obstruction groups to the coarse Baum–Connes conjecture can also be derived from the dual localization algebras.